Question

If n is the sample size and x is the number in the sample who have a certain characteristic, then x/n is called the sample [blank]
Answer
The probability distribution of p is called a [blank] distribution.
Answer
The probability distribution of ^p is called a [blank] distribution.
Answered by GPT-4o mini
If \( n \) is the sample size and \( x \) is the number in the sample who have a certain characteristic, then \( \frac{x}{n} \) is called the sample **proportion**.
Answered by GPT-4o mini
The probability distribution of \( p \) is called a **binomial** distribution, if \( p \) represents the probability of success in a binomial experiment (which consists of a fixed number of independent trials, each with two possible outcomes). If \( p \) is being considered in a different context, it could also be related to other distributions (e.g., normal or uniform), but in the context of sample proportion and successes in trials, the term “binomial” is most applicable.
Answered by GPT-4o mini
The probability distribution of \( \hat{p} \) (the sample proportion) is called a **sampling distribution**. Specifically, when the sample size is large, the sampling distribution of \( \hat{p} \) can be approximated by a **normal distribution** due to the Central Limit Theorem, especially when the conditions for the normal approximation are met (e.g., \( np \) and \( n(1-p) \) both being greater than 5 or 10).